Classical and quantum kinetic equations with exact conservation laws

Stationary and dynamic properties of reduced density matrices can be determined from formal or approximate closures of an infinite hierarchy of equations. The local macroscopic conservation laws place weak but important constraints on the reduced density matrices which should be respected by any closure. For pairwise additive forces conditions on the closure of the one- and two-particle equations are obtained that preserve the exact functional dependence of the conserved densities and their fluxes on the reduced density matrices. To illustrate the nature of these conditions, a closure approximation suitable for a quantum gas is given, yielding an extension of the time-dependent Hartree-Fock equations for the dynamics of a nuclear fluid to include collisions.     

An efficient parallel high-order compact scheme for the 3D incompressible Navier–Stokes equations

This article provides a strategy for solving incompressible turbulent flows, which combines compact finite difference schemes and parallel computing. The numerical features of this solver are the semi-implicit time advancement, the staggered arrangement of the variables and the fourth-order compact scheme discretisation. This is the usual way for solving accurately turbulent incompressible flows. We propose a new strategy for solving the Helmholtz/Poisson equations based on a parallel 2d-pencil decomposition of the diagonalisation method. The compact scheme derivatives are computed with the parallel diagonal dominant (PDD) algorithm, which achieves good parallel performances by introducing a bounded numerical error. We provide a new analysis of its effect on the numerical accuracy and conservation features. Several numerical experiments, including two simulations of turbulent flows, demonstrate that the PDD algorithm maintains the accuracy and conservation features, while conserving a good parallel performance, up to 4096 cores.     

工科学校本科生科研训练与实践——以节能减排大赛为例

科研训练是本科生学习中必不可少的一个环节,在提升学生知识运用、科学素养等方面有着重要作用。本文将以"大学生节能减排大赛"的参赛过程为例,从学生的视角简要介绍高分子材料与工程专业本科生的科研训练,以及如何结合学科以及学校特色,将所学知识用于解决实际问题。     

How mobile NMR can help with the conservation of paintings

The conservation of paintings is fundamental to ensure that future generations will have access to the ideas of the grand masters who created these art pieces. Many factors, such as humidity, temperature, light, and pollutants, pose a risk to the conservation of paintings. To help with painting conservation, it is essential to be able to noninvasively study how these factors affect paintings and to develop methods to investigate their effects on painting degradation. Hence, the use of mobile nuclear magnetic resonance (NMR) as a method of investigation of paintings is gaining increased attention in the world of Heritage Science. In this mini-review, we discuss how this method was used to better understand the stratigraphy of paintings and the effect different factors have on the painting integrity, to analyze the different cleaning techniques suitable for painting conservation, and to show how mobile NMR can be used to identify forgeries. It is also important to keep in mind its limitations and build upon this information to optimize it to extend its applicability to the study of paintings and other precious objects of cultural heritage.     

Preliminary study of UV ageing process of proteinaceous paint binder by FT-IR and principal component analysis

This work presents a preliminary study on the ageing process of proteinaceous binder materials used in painting under UV light. With this aim, two sets of model samples were prepared: samples prepared using a single protein material and complex samples prepared in a similar way to the sequence of layers in a real painting from lowest to highest complexity (protein, drying oils, pigment and varnish). The study focuses on acquiring information about the possible degradation process of proteinaceous binders due to ageing and how this process be affected by the presence of characteristic non-proteinaceous painting materials, such as lipids from linseed oil, terpenic compounds from varnish and inorganic pigments. Samples simulated the accelerated ageing process, as did the UV light exposition. The FT-IR spectra were recorded after 100, 500, 1000 and 1500 h of exposition. The study of the accelerated ageing process was performed by means of principal component analysis (PCA) using the FT-IR spectra obtained. Loadings from the significant principal components were analysed to find the FT-IR frequency (cm⁻¹) involved in the degradation process. The study showed the lack of any relevant modification on the proteins in the single model samples. On the contrary, the complex model samples showed the ageing process. The accelerated ageing process can be explained by a principal component from PCA. The most affected IR region was 2900-3600 cm⁻¹, where the amide band was included.     

Fourier transform infrared spectroscopy and the analytical study of works of art for purposes of diagnosis and conservation

This paper is a study of the analytical capacity of Fourier transform infrared spectroscopy (FT-IR) for any type of samples from works of art. The analytical information obtained with this technique on organic and inorganic compounds is extremely useful in the preliminary studies necessary for diagnosis and to decide on the conservation process. This paper reports the analysis and study with FT-IR on samples extracted from the microlayers in several works of art from different periods (16th to 18th century) comprising wall paintings and canvas. The most outstanding of these being the frescoes by A. Palomino from two ceilings in the Santos Juanes church. The analytical procedures for the different components of the works studied such as

1. (a) varnish applied to wood panels and canvas paintings,

2. (b) binding media and pigments used by the artists,

3. (c) inerts, mortars, stuccos and grounds have been optimized. The FT-IR technique offers a quick analysis of microsamples (less than 0.5 mg) and is able to characterise the different molecular groups which provide information on the nature of the different materials of organic and inorganic origin used by the artist and thus permits the diagnosis of pathologies requiring conservation treatment.

A conservative unstructured scheme for rapidly varied flows

This article introduces a new semi‐implicit, staggered finite volume scheme on unstructured meshes for the modelling of rapidly varied shallow water flows. Rapidly varied flows occur in the inundation of dry land during flooding situations. They typically involve bores and hydraulic jumps after obstacles such as road banks. Near such sudden flow transitions, the grid resolution is often low compared with the gradients of the bathymetry. Locally the hydrostatic pressure assumption may become invalid. In these situations, it is crucial to apply the correct conservation properties to obtain accurate results. An important feature of this scheme is therefore its ability to conserve momentum locally or, by choice, preserve constant energy head along a streamline. This is achieved using a special interpolation method and control volumes for momentum. The efficiency of inundation calculations with locally very high velocities, and in the case of unstructured meshes locally very small grid distances, is severely hampered by the Courant condition. This article provides a solution in the form of a locally implicit time integration for the advective terms that allows for an explicit calculation in most of the domain, while maintaining unconditional stability by implicit calculations only where necessary. The complex geometry of flooded urban areas asks for the flexibility of unstructured meshes. The efficient calculation of the pressure gradient in this, and other semi‐implicit staggered schemes, requires, however, an orthogonality condition to be put on the grid. In this article a simple method is introduced to generate unstructured hybrid meshes that fulfil this requirement. Copyright © 2008 John Wiley & Sons, Ltd.     

A volume-amending method to improve mass conservation of level set approach for incompressible two-phase flows

A volume-amending method is developed both to keep the level set function as an algebraic distance function and to preserve the bubble mass in a level set approach for incompressible two-phase flows with the significantly deformed free interface. After the traditional reinitialization procedure, a vol-ume-amending method is added for correcting the position of the interface according to mass loss/gain error until the mass error falls in the allowable range designated in advance. The level set approach with this volume-amending method incorporated has been validated by three test cases: the motion of a single axisymmetrical bubble or drop in liquid, the motion of a two-dimensional water drop falling through the air into a water pool, and the interactional motion of two buoyancy-driven three- dimensional deformable bubbles. The computational results with this volume-amending method in-corporated are in good agreement with the reported experimental data and the mass is well preserved in all cases.     

Spectral Semi-discretisations of Weakly Non-linear Wave Equations over Long Times

The long-time behaviour of spectral semi-discretisations of weakly non-linear wave equations is analysed. It is shown that the harmonic actions are approximately conserved for the semi-discretised system as well. This permits to prove that the energy of the wave equation along the interpolated semi-discrete solution remains well conserved over long times and close to the Hamiltonian of the semi-discrete equation. Although the momentum is no longer an exact invariant of the semi-discretisation, it is shown to be approximately conserved. All these results are obtained with the technique of modulated Fourier expansions. Dedicated to Professor Arieh Iserles on the Occasion of his Sixtieth Birthday.